Learning radical excited states from sparse data

Abstract

Emissive organic radicals are currently of great interest for their potential use in the next generation of highly efficient organic light emitting diode (OLED) devices and as molecular qubits. However, simulating their optoelectronic properties is challenging, largely due to spin-contamination and the multiconfigurational character of their excited states. Here we present a data-driven approach where, for the first time, the excited electronic states of organic radicals are learned directly from experimental excited state data, using a much smaller amount of data than typically required by Machine Learning. We adopt ExROPPP, a fast and spin-pure semiempirical method for the calculation of the excited states of radicals, as a surrogate physical model for which we learn the optimal set of parameters. To achieve this we compile the largest known database of organic radical geometries and their UV-vis data, which we use to train our model. Our trained model gives root mean square and mean absolute errors for excited state energies of 0.24 and 0.16 eV respectively, improving hugely over ExROPPP with literature parameters. Four new organic radicals are synthesised and we test the model on their spectra, finding even lower errors and similar correlation as for the training set. This paves the way for the high throughput discovery of next generation radical-based optoelectronics.

Fig. 1. Structures of the molecules in the training set containing carbon, hydrogen, chlorine and pyrrole-type nitrogen. The central TTM/PTM backbone is coloured in grey, and substituents colored in light blue.

Fig. 2. Structures of the molecules in the training set containing aniline, pyridine and multiple types of nitrogen. The central TTM/PTM backbone is coloured in grey, and substituents colored in light blue.

Fig. 3. A flow diagram illustrating our method for training our ExROPPP model on the experimental absorption data of organic radicals.

Fig. 4. Regression plots of the excited state energies of the 81 molecule training set calculated by ExROPPP compared with experimentally determined energies, using parameters obtained from the literature (left) and those of the trained ExROPPP model (right). The trained model predicts the energies of UV/visible absorptions much closer to experiment (red line) than do the literature parameters.

Fig. 5. UV-visible absorption spectra of TTM-1Cz and TTM-1Cz-An measured in 200 μM toluene solution at room temperature (red), simulated using ExROPPP with literature parameters (blue) and with the trained 81 molecule model (black). The trained model substantially improves on the literature parameters in both cases.

Fig. 6. Structures of the four newly synthesised radicals reported in this work: M₂TTM-4T, M₂TTM-3PCz, M₂TTM-3TPA and M₂TTM-4TPA, which constitute the testing set.

Fig. 7. HOMO of TPA calculated by closed-shell PPP (with the optimised parameters obtained from training on 81 radicals). There is significant HOMO amplitude at the para (4) position but minimal amplitude at the meta (3) position, such that the design rules correctly predict M₂TTM-4TPA to have a significant low-energy visible absorption and M₂TTM-3TPA not to have one.

Fig. 8. UV-visible absorption spectra of the newly-synthesised M₂TTM-4T (top left), M₂TTM-3PCz (top right), M₂TTM-3TPA (bottom left) and M₂TTM-4TPA (bottom right) measured in 0.1 mM toluene solution (red), simulated using ExROPPP with literature parameters (blue) and of the trained 81 molecule ExROPPP model (black). Trained ExROPPP (black) reproduces the experimental spectra (red) more accurately than untrained ExROPPP with literature parameters (blue).

Fig. 9. Regression plot of the excited state energies of the radicals in the testing set calculated by ExROPPP and compared with experimentally determined energies. ‘lit.’ refers to the parameters sourced from the literature and ‘ML’ refers to the parameters of the trained 81 molecule model. It can be clearly seen that for this testing set the trained ExROPPP model more accurately reproduces the experimental values than ExROPPP with literature parameters.